The Fundamental Geometry of Cutting Tools

Abstract

A full geometrical analysis of a cutting tool edge is made, in which an effective rake of universal application is defined in terms of the primary rake and the angle of obliquity of the edge. The fundamental angles are related in an easy manner to the traditional workshop terms, and may readily be applied to any cutting tool. A law of chip flow is given and its effects on the resulting chip shape are analysed. The effect of unit cube passing through the shear plane is also analysed and a method is given of finding the direction cosines of the axes of the ellipsoid of stress. The flow law is used to find the directions ofthe cutting force between chip and tool and its various components. An examination of velocity and force diagrams for oblique cutting in Merchant's shear theory leads to a debatable result at variance with his fundamental machining equation. Although predominantly theoretical, the paper has a practical background.